In York, single parent families account for half of those in urgent housing need. Over 70% of lone parents in York are living in poverty and are amongst the hardest hit by the lack of affordable housing.

The city council is well aware of the issue, which York Welfare Campaign is now highlighting by collecting individual evidence. I went to talk to 24-year-old Laura Wade who lives in a damp one bedroom apartment with her 12 month old daughter.

She contacted the Campaign when other single mothers began posting about their situation on a mums' internet site. She says:

Somebody inboxed me about it. A lot of mums are posting that they are in one bedroom properties with a child and can't get anything else.

It is virtually impossible to find a two bedroom property within miles of York city centre that is on or below the benefit cap of £524 per calendar month. The Local Housing Allowance means that only three in every ten properties are affordable to people in receipt of housing benefit. In reality, the proportion is probably smaller because most landlords prefer to have tenants in full time employment.

That isn't prejudice, a local estate agent whom I interviewed told me. Many landlords would be happy to consider benefit claimants but housing benefit is often paid late, in arrears, and every four weeks, causing problems for landlords who pay their buy-to-let mortgages every calendar month and incur heavy penalities if payments are delayed.

A few yards away from Laura's flat, about a dozen estate agents advertise two bedroom properties that would be perfect for this young mum and her little girl. The trouble is, none of them are affordable on the Local Housing Allowance. I asked in several estate agents if there were any properties available that did and was told that there were – occasionally. Not one estate agent had a property currently within the benefit price range and the average for a two bedroom house was £676 per month. There were 63 two bedroom properties available for rent in York last month. All but two cost more than the benefit cap.

Helen Graham from the York Welfare Campaign says:

At one time people might have been able to subsidise rent out of benefits but you can't now. Everything's gone up and the cost of living is rising steadily while tax credit has been cut. It's all just bearing down on people.

Laura's postage stamp flat is dark,damp and cold although she's tried to make the best of it. Her daughter has been admitted to hospital on 11 separate occasion in the past nine months with chest infections. Her GP and health visitor have written to the landlord and the council supporting her application for a transfer. The landlord isn't an investor or Dickensian character trying to pick a pocket or two but a housing association who paid their chief executives an average of £167,500 per year.

Laura acquired the tenancy after spending months in a hostel fleeing domestic violence. At first, the damp didn't bother her – she was just glad to have a roof over her head. But when she discovered extensive mould over her baby's cot mattress she began to worry.

She can't move. She is classed as being in the highest level of need but it will be years before she will be offered a suitable property and she's been advised to stick it out. It's unlikely that she would be able to save £1500 for a deposit to rent privately from her benefits. Helen Graham says:

In a city where there is insufficient affordable housing and landlords are unwilling to rent out to benefit claimants where are people like Laura to go?

Laura says:

The damp in the bedroom is the problem. It's all over the mattress and even after its been scrubbed, you just can't remove it.

She cleans a lot – it's something to do and the flat is immaculate except for bags and bags of clothes and toys that can't be stored in an enclosed space without succumbing to the damp. I begin to cough constantly despite the warm sunshine outside the window.

Laura smiles.

It's cold all the time and the heating takes about an hour to kick in. At five in the afternoon I need to turn on the heating to heat the room up for seven when my daughter goes to bed. Outside it's 70 degrees but in the flat it could be the middle of winter.

She laughs. Even the maintenance manager comments that it's always warmer outside.

Laura wants to work for the ambulance service but can't because her daughter always has a bad chest because of the damp and the nurseries she has tried won't give children medication. The cost of childcare in York is meanwhile so high that low paid single parents cannot afford it. It is becoming harder and harder for women like her to work their way out of poverty.

She says:

It's difficult to live on what I get at the moment. My nan and granddad help me out a lot – buying nappies or if I need some shopping, but I don't like relying on them all the time. That's why I really want to go out and work. During the day, I'm kept busy but when the baby's in bed and you're sat down thinking, I just can't work out of it. There's no room for manoeuvre.

She admits to often feeling depressed and has 'gone to the doctor for anti depressants but not said anything.'

Laura Wade and her daughter at home. Clothes and toys have to be bagged because of pesistent damp. Photograph: Anne Czernik

Laura was surprised to find herself expecting shortly after moving into the tiny flat. She was working and had taken every precaution to prevent pregnancy. She is clearly devoted to her daughter and with a level two qualification in childcare is a knowledgeable parent.

Following the birth, she lived at her mother's until her daughter was three months old, but returned to the flat after the housing association threatened to end the tenancy if she did not occupy the property. She remembers how her daughter deteriorated and needed frequent treatment for chest infections.

When she was admitted into hospital at Xmas, she was on oxygen for a week, with nebulisers and heart machines and stuff. She was really poorly. They said that if she didn't pick up on her feeding (she was being fed through tubes) she wouldn't be home in time for Christmas

Luckily the child recovered and was discharged on Christmas Eve - to celebrate her first Christmas in a modern slum. Laura says of her daughter's frequent infections:

It makes me feel really bad. What if they ring social services on me? It's really hard.

Laura just wants to get her life on track, retrain and find a job.She feels that she 'can't do it with things as they are' and it's easy to see why she feels trapped by her situation.

When I ask her what would be her ideal solution, I expect the asnwer to be a dream house and a Lottery win. Instead, she just wants:

A new place with two bedrooms. I'm not that bothered about a garden as long as it's a two bedroom place that was damp free. If I had the choice between a lot of money – a couple of grand or something – or a new place, it's the new place I'd go for.

Anne Czernik is a freelance photojournalist specialising in activism in the north of England.